JAMAICA_9th Grade Math Table of Content with Listing of Activities

Transcription

1 JAMAICA_9th Grade Math Table of Content with Listing of Activities 1. Number System 1.1 Introduction Tutorial: Introduction Example: True/False (1) Example: Find 2 rational numbers between given integers (1) Example: Find 3 rational numbers between given integers (2) Example: Find 3 rational numbers between given rationals (3) Example: Find 3 rational numbers between given rationals Example: Find 5 rational numbers between given rationals Example: Find 6 rational numbers between given integers Test your Skill 1.2 Real Numbers and their Decimal Expansions Tutorial: Real Numbers and their decimal expansions Example: Express the real number of the form p/q as repeating decimal (1) Example: Terminating/Non terminating decimal Example: Rational/Irrational 1.3 Representing real numbers on the number line Tutorial: Representing real numbers on the number line 1.4 Laws of Exponents for Real Numbers Tutorial: Laws of Exponents for Real Numbers Example: Simplify: 11^1/2/11^1/4 Example: Find the value: (64)^1/2 Example: Simplify: 2^2/3 * 2^1/5 Example: Simplify: (2)^2/3 * (2)^1/3 Example: Simplify: 7^1/2 * 8^1/2 1.5 Expressing Numbers in the Standard Form

2 Tutorial: Expressing Numbers in the Standard Form Example: Express the decimal number in standard form (5) Example: Express the decimal number in standard form (5) Example: Express the number in standard form Example: Application based on expressing numbers in the standard form 2. Comparing Quantities 2.1 Understanding Ratios Tutorial: Understanding Ratios Example: Reduce the given ratio in lowest term (1) Example: Application: Based on comparison of ratios (2) Example: Application: Based on comparison of ratios (3) Example: Application: Based on comparison of ratios (3) Example: Application : Based on comparison of ratios (2) Example: Find the ratio of given numbers (4) Example: Determine whether the given ratios are equivalent Example: Find the ratio of dollars to cents Example: Find the ratio of kg to gm Example: Find the ratio of days to hours Application: Divide the amount in the given ratio Test your Skill 2.2 Unitary Method Tutorial: Unitary Method Example: Application: Based on unitary method (1) Example: Application: Based on unitary method (1) Example: Application: Based on inverse variation (2) Example: Find the actual distance between two places in km, given distance in cm Example: Application: Based on unitary method Example: Application: Based on unitary method Example: Application: Based on unitary method

3 Test your Skill 2.3 Checking Proportions Tutorial: Checking Proportions Example1: Verifying Proportions 2.4 Solving Proportions Tutorial: Solving Proportions Example1: Finding a missing term in a Proportion Example2: Finding a missing term in a Proportion Example3: Finding a missing term in a Proportion 2.5 Solving Applications Using Proportions Tutorial: Solving Applications Using Proportions Example: Application of Proportion : Field Problem Example: Application of Proportion : Distance Problem Example: Application of Proportion : Mixture Problem Example: Application of Proportion : Basic Problem Application: Application of Proportion : Height of Tree Problem 2.6 Understanding Percents Tutorial: Understanding Percents Example: Find what percent of given figure is shaded (2) Example: Find what percent of given figure is shaded (2) Example: Application problem based on percentage (1) Test your Skill 2.7 Ratios to Percents Tutorial: Ratios to Percents Example: Application problem based on percentage (1) Example: Application problem based on percentage (2) Example: Find the angles of triangle if their ratios are given. Example: What percent is "a gm" of "b kg"? Example: Convert each part of the ratio to percentage Application: Problem based on percentage (2)

4 Application: Problem based on percentage Test your Skill 2.8 Converting Percentages to Fractions or Decimals and Vice Versa Tutorial: Converting Percentages to Fractions or Decimals and Vice Versa Example: Application problem based on percentage (4) Example: Convert the decimal number in to percentage (2) Example: Convert the percentage in to decimal number (3) Example: Convert the mixed fraction in to percentage (1) Example: Convert the percentage in to fraction (3) Example: Find in percent the portion of the given figure which is coloured Application: Word problem based on percentage (2) Application: Find the percentage of children in a city Application: What percent of students do not have bicycles? Application: Find the percentage of voters who did not cast their votes 1 2 Test your Skill1 Test your Skill2 2.9 Problems on Percentage Tutorial: Problems on Percentage Example: Find the percentage of the integer (1) Example: Application problem based on percentage (2) Example: Application problem based on percentage (2) Example: Application problem based on percentage (2) Example: Find the percent increase in population (2) Example: Find the total amount if A% of it is B? Example: Find the number whose A% is B Application: Find the left amount after deductions (2) Application: Find maximum marks if % and marks secured are known (2) Application: Word problem based on percentage (2)

5 Application: Find the number of boys if number of girls and % of boys are given (3) Application: Word problem based on percentage (3) Application: Find monthly income if % expenditure is given (3) Application: Find number of student before and after increase (3) Application: Word problem based on percentage (2) Application: How much matches were won by football team? Application: Find the salary, given the savings and percent of savings Application: Divide chocolates between two persons so that they get a% & b% of them Application: Find the percentage decrease of population of a city Test your Skill 3. Sets 3.1 Sets and Set Notations Tutorial: Sets and Set Notations Example: Change set builder form to list form Example: Change set builder form to list form Example: Change set builder form to list form Example: Change set builder form to list form Example: Change list form into set builder form Example: Change list form into set builder form Example: Change list form into set builder form Example: Change set builder form into roster form Example: Write the given statement into roster form and set builder form Types of Sets Tutorial: Types of Sets Example: Identify the given set as finite or infinite Example: Identify the given set as empty set or singleton set 1

6 3.3 Subsets Tutorial: Subsets Example: Identify the given statement is true or false Example: Identify the given statement is true or false Example: Identify whether given statement is true or false Example: Identify whether given statement is true or false Example: Find the number of subsets Operations on Sets Tutorial: Operations on Sets Example: Find the union and intersection of two given sets Example: Find the difference of two sets Example: Find the union and intersection of two given sets Example: Find the union and intersection of three given sets Example: Find the complement of given set Example: Find the complement of given set Example: Find the complement of intersection of two sets Venn Diagrams Tutorial: Venn Diagrams Example: Find the number of elements in intersection of two sets Example: Represent given sets in a venn diagram Example: Find the sets from the given venn diagram Example: Find union and intersection using venn diagram Example: Find the intersection 1

7 4. Measurements 4.1 Basic Operations on Measurements Multiplying and Dividing Measurements by Numbers Tutorial: Multiplying and Dividing Measurements by Numbers Example1: Multiply a Measurement by a Number Example2: Multiply a Measurement by a Number Example3: Dividing a Measurement by a Number Example4: Multiply a Measurement by a Number Adding and Subtracting Measurements Tutorial: Adding and Subtracting Measurements Example1: Adding Measurements of same Unit Application1: Adding and Subtracting Measurements 4.1 Section Review Practice Test your Skill 4.2 Unit Conversions in the Same System Converting Units in the Metric System Tutorial: Converting Units in the Metric System Example1: Conversions in Metric: Liters to Milliliters Example2: Conversion in Metric: Meter per liter to kilometer per centiliter Application2: g to mg 4.3 Estimating Measurements in the Metric System Estimating Measurements in the Metric System Tutorial: Estimating Measurements in the Metric System Example1: Identify Metric Unit 4.3 Section Review Practice Test your Skill 5. Perimeter and Area 5.1 Perimeter of Plane Figures Tutorial: Perimeter of Plane Figures

8 Example: Wire in shape of rectangle is rebent in shape of square, find measure of each side 5.2 Area of Plane Figures Tutorial: Area of Plane Figures Example: Find area enclosed by given triangle Example: Find height of a right triangle whose area & base are given Example: Find altitude drawn from vertex of right angled on its hypotenuse Example: A square is placed inside rectangle, find area of region inside rectangle that surrounds square Example: Find area of region given in figure Example: The perimeter & breadth of rectangle are given, find its length & area Example: Find breadth of rectangular park if area of square & rectangular park are same Example: Base of //gm is twice its ht., if area is given, find base and ht. Example: Ht. corresp. to base AB of //gm ABCD is given, find ht. corresp. to base BC Example: Perimeter of triangular field & ratio of its sides are given, find its area Example: Find length of altitude in given triangle Example: Find the area of a triangle,whose sides are given Example: Find area of triangle, whose two sides and perimeter are given Pythagoras Theorem Tutorial: Pythagoras Theorem Example: Find distance from starting point Example: Find length of ladder Example: Find width of street if ladder is turned around Example: Find distance of foot of ladder from base of wall Example: Find length of side (2 right angled triangles) Example: Find length of hypotenuse from given figure

9 Practices Test1 6. Volume 6.1 Volume of a Cuboid and a Cube Tutorial: Surface area and volume of a cuboid and a cube Example: Find the height of cuboid when its volume and area of its base is given (1) Example: Find surface area of a cube when its volume is given (1) Example: Find the surface area of cuboid made by joining 3 cubes (2) Example: Find dimensions of cuboid when its TSA & ratio of sides are given (2) Example: Find volume of cuboid when area of four walls & height is given (3) Example: Find the dimensions of a cuboid when difference in covering rates are given (4) Example: Find area of base of cuboid when its TSA and LSA are given (2) Example: Find the TSA of all small cubes made from a big cube (2) Example: Find volume of box formed by folding a sheet (2) Example: How many cubes can be placed in a box? (2) Example: Application problem based on the volume water falling into sea (5) Example: Find the area of sheet required to make a box & cost of sheet Example: Find the ht. of the wall of a rectangular hall Example: How many bricks can be painted out of the container? Example: Which box has larger LSA & smaller TSA? Example: How much tarpaulin is required to make a shelter of given dimensions? Example: Find the area of the glass Example: Find the cost of cardboard required for supplying given no. of boxes Example: Determine the dimensions of the box Example: Determine the cost of painting inner surface of the box Example: Determine length & breadth of a box Example: Determine the cost of distempering the walls of a hall from inside Example: Determine the breadth & height of a water tank Example: Determine how much level of piece of land will be raised Example: How much high would the cubical vessel be made to hold given quantity of liquid? Example: Find the number of bricks

10 Example: Find the volume of the structure build by the child Example:Determine the rise in water level Example: For how many days the water of given tank lasts Example: Determine the weight of wood Example: Find the speed of flowing petrol Example: Find the area irrigated Example: Find the area irrigated Test your Skill 6.2 Volume of a Right Circular Cylinder Tutorial: Surface area and volume of a right circular cylinder Example: Find diameter of cylinder when its CSA and height are given (1) Example: Find cost of painting a cylindrical pillar (3) Example: Find number of rods which can be made from given mass of iron (3) Example: Find area of sheet required to make a cylindrical tank (2) Example: Find area leveled by a roller (2) Example: Find capacity of a cylindrical vessel (3) Example: Find volume of cylinder when its CSA and height are given (4) Example: Find radius of cylinder when its volume and ratio of r:h are given (4) Example: Find ratio of volumes of 2 cylinders given ratio of their radii & heights (4) Example: Find ratio of volumes of reduced cylinder to original cylinder (4) Example: Find length of wire given CSA of cylinder & diameter of wire (4) Example: Find the inner SA, outer SA & TSA of metal pipe Example: Find the ht. of a cylinder given its CSA and radius of its base Example: Find the area of chart paper required to make cylindrical kaleidoscope Example: Find the total radiating surface in the system Example: Find the inner CSA & cost of plasting this curved surface Example: Find the CSA of a closed cylinder

11 Example: Find how much cloth is req. for covering the lampshade Example: How much cardboard was req. to be bought for the competition? Example: Determine the ratios of the volume of two cylinders Example: Determine the timber that can be obtained from the log of wood Example: Determine the cost of leveling Example: Which tin has more capacity Example: How much concrete mixture is required to build cylindrical pillar? Example: How much money does stall keeper receive by selling the juice completely? Example: Find the mass of the pipe Example: Which container has greater capacity and by how much? Example: Find the inner CSA, radius of base & capacity of the vessel Example: Find the volume of the wood & that of graphite Example: How much soup the hospital has to prepare daily to serve patients? Example: Determine the height of embankment Example: Determine the diameter of the base of a new solid cylinder Example: Determine the cost of excavation of the cylindrical hole Example: Find the outer and inner radii of the pipe Test your Skill 7. Time and Temperature 7.1 Convert Temperatures from Celsius to Fahrenheit Tutorial: Convert Temperatures from Celsius to Fahrenheit Example: Convert 'Fahrenheit' to 'Celsius' Example: Convert 'Fahrenheit' to 'Celsius' & vice versa 8. Angles and Parallel Lines 8.1 Geometry Terminology Tutorial: Geometry Terminology Example: Count no. of points & line segments in given figure Example: Check if lines are intersecting/parallel in given figure Example: Find no. of rays in given figure Example: Name line segment(s) & ray(s) in given figure

12 8.2 Angles and its Types Tutorial: Angles and its Types Example: Identify type of angle Example: Count number of acute & right angles in given figure 8.3 Pairs of Related Angles Tutorial: Pairs of Related Angles Example: Find complement of given angle Example: Find supplement of given angle Example: Find measure of unknown angles Application: True or False Application: Find measure of supplementary angles satisfying given condition Application: Find measure of complementary angles satisfying given condition 8.4 Constructing Angle and Angle Bisector Tutorial: Constructing Angle and Angle Bisector 8.5 Constructing Angles : 60, 30, 120, 90,45 Tutorial 8.6 Constructing Perpendicular and Perpendicular bisector Tutorial: Constructing Perpendicular and Perpendicular bisector 8.7 Parallel Lines and Special Angle Pairs Tutorial: Parallel Lines and Special Angle Pairs Example: Find value of x if l is parallel to m Example: Find angles given lines are parallel Example: Find measure of angle from given figure, arms of angles are parallel

13 Polygons: Triangles and Quadrilaterals 9.1 Introduction Tutorial: Introduction Example: State correspondence between sides of Congruent Triangles (1) Example: State correspondence between angles of Congruent Triangles (2) Example: Find the value of 'm' in the given triangle (3) 9.2 Criteria for Congurence of Triangles Tutorial 1 : Criteria for Congruence of Triangles I Tutorial 2 : Criteria for Congruence of Triangles II Example: Find length of side of triangle using Congruence Property of triangles (2) Example: Find length of required side of triangle using ASA Congruence Property of triangles (2) Example: Find side of triangle using AAS rule/property (2) Example: Find perimeter of quadrilateral using ASA property (3) Example: Find length of required side in given figure using Congruence Property of triangles (2) 9.3 Properties of a Triangle Tutorial: Properties of a Triangle Example: Find the value of required angles in Isosceles Triangle (2) Example: Problems based of sides of Isosceles Triangle (1) Example: Find the value of required angle in the Isosceles Triangles (5) Example: Find the value of required angles in Isosceles Triangle (4) Example: Find the value of required angles in Isosceles Triangle (3) Example: Find the value of required side in Isosceles Triangle (5) Example: Find the value of required angle in Isosceles Triangle (3) 9.4 Construction of Triangles Tutorial: Construction of Triangles Tutorial: Construction of Triangles

14 9.5 Regular Polygons and Measure of Angles Tutorial: Regular Polygons and Measure of Angles Quadrilateral Tutorial: Quadrilateral Example: Find measure of fourth angle of quadrilateral Example: Find measure of four angles of quadrilateral Types of Quadrilaterals Tutorial: Types of Quadrilaterals Example: Find measure of angle using properties of square Example: Find angle using properties of rectangle 9.8 Sufficient Conditions for a Quadrilateral to be a Parallelogram Tutorial: Sufficient Conditions for a Quadrilateral to be a Parallelogram 9.9 Properties of a Parallelogram Tutorial: Properties of a Parallelogram Example: Given perimeter & longer side, find measure of shorter side of //gm Example: Find value of x & y from given parallelogram Example: Find angle in given parallelogram Example: Find measure of side using property of bisection of diagonals Example: Find measures of angles of parallelogram Construction of Quadrilaterals Tutorial: Construction of Quadrilaterals when four sides and one diagonal are given Tutorial: Construction of Quadrilaterals when three sides and two diagonals are given Tutorial: Construction of Quadrilaterals when three angles and two included sides are given

15 Tutorial: Construction of Quadrilaterals when three sides and their included angles are given Tutorial: Construction of Quadrilaterals when its four sides and one angle are given 10. Circles 10.1 Circles and its Related Terms Tutorial: Circles and its Related Terms Tutorial: Circles and its Related Terms Chords of a Circle and its Related Theorems Tutorial: Chords of a Circle and its Related Theorems Example: Given radius and length of chord, find distance of chord from centre (2) Example: Find length of chord if its distance from centre & radius of circle are known (2) Example: Given length of chords & radius, find distance btw 2 chords on same side of centre (4) Example: Given length of chords & radius, find distance btw 2 chords on either side of centre (4) Example: Given length of chords & distance btw them, find radius of circle (4) Example: Find length of a chord from given figure (2) Perimeter Tutorial: Perimeter & Area of a Circle Example: Find radius of circle whose circumference equals sum of circumference of 2 circles of given radii (2) Example: Find number of revolutions made by wheel in given time, if speed is known (3) Example: Find diameter of a protractor if perimeter is known (2) Example: Find area of a circle whose circumference is known (2) Example: Find the cost of fencing a circular track (2) Example: Find area of quadrant if circumference is known (2) 10.4 Area of Sector and Segment of a Circle Tutorial: Area of Sector and Segment of a Circle Example: Find area of shaded region (square with circle at each corner) (3)

16 Example: Find area between two consecutive ribs of an umbrella (4) Example: Find area covered by minute hand (3) Example: Find area of triangular plot which can be grazed by horses (3) Example: Find area of minor and major segments (4) Example: Find area of shaded region (quadrant and semicircle) (5) Example: Find area of sea over which ships are warned (3) Example: Find area cut off from each vertex of a trapezium (1) Example: Example: Example: Find length of an arc if area is known (2) Example: Find radius of circle if arc and area of sector it bounds is known (4) Example: Find area between sectors of two concentric circles of given radii (3) Example: Find area cleaned by wiper blades (4) Example: Find radius of circle if length of arc is known (3) Example: Find area of sector (2) Example: Find area of 4 corners of a rectangle (1) Example: Find ratio of areas of two sectors (2) Example: Find ratio of length of arc to the circumference of the circle (2) 11. Solids/Three Dimensional Figures 11.1 Visualising Shapes Tutorial: Visualising Shapes Example: Identify top, front, side views of given solid (3) 11.2 Faces, Vertices and Edges Tutorial: Faces, Vertices and Edges Example: Identify top, side, front views of the given solid (3) Example: Using Euler's formula, find the unknown value (3) Example: Can a polyhedron have given number of faces, edges & vertices? (2) Example: identify the given figure

17 11.3 Prism Tutorial: Prism Example: Find LSA & TSA of a right prism of triangular base Example: Find LSA, TSA & volume of a right prism Example: Find LSA & TSA of a prism of equilateral triangular base with given side& given the volume of prism Example: Find LSA & TSA of a prism of isosceles triangular base with given sides & given the volume of prism Example: Find the cost of making a wooden box in the shape of a triangular prism whose base is rt. triangle Example: Find the cost of tiles required for lateral faces of n pillar Example: How much would the company pay for the advertisement on the walls of pillars in shape of triangular prism Example: Find LSA & TSA of a prism of equilateral triangular base with given side& given the ht. of prism Example:Find LSA & TSA of a prism of rt. triangular base with given side & area of base & volume of prism Example: Find LSA of the prism given the perimeter of the base & its height Example: Find the length of each side of base of prism given the area of base(equilateral triangle) 11.4 Volume of Cuboid and Cube Tutorial: Volume of Cuboid and Cube Example: Find the volume of rectangular solid with given dimensions.(1) Example: Find the volume of a cube whose side is given.(1) Example: Find in litres, the volume of a storage tank whose length, breadth & depth are given.(2) Example: Find the depth of a tank, when its volume and dimensions are given.(3) Example: Find the increase in volume, when its edge is doubled.(4) Example: Find surface area of a cuboid, when its volume and two sides are given.(4) Application: Based on volume of a cuboid.(5)

18 : Volume of Cuboids and Cubes 11.5 Surface area and Volume of a Right Circular Cylinder Tutorial: Surface area and Volume of a Right Circular Cylinder Example: Find diameter of cylinder when height & CSA are given (1) Example: Problem based on curved surface area and cost of cylinder (2) Example: Find the area of a cylinder when diameter and height are given (1) Example: Application based on area of cylinder when diameter & height are given (2) Example: If ratio of radius, height & volume of cylinder are given then find radius (2) Example: If LSA of cylinder is given & if cylinder is cut in form of rectangle,find perimeter of rectangle if width is known (3) Example: Application based on volume of cylinder (2) Example: Find area of label around surface of cylindrical container, given height, base diameter & where label is placed (5) Example: Identify which box has larger surface area Example: Application based on area of cylinder Example: Find the volume & surface area of cylinder when dimensions are given Example: Find the quantity of milk in tank when radius & height are given 12. Symmetry 12.1 Symmetry Tutorial: Symmetry Example: Choose the fig. with exactly 1 line of symmetry Example: Choose the alphabet which does not possess linear symmetry Example: Choose the alphabet having exactly one line of symmetry 12.2 Symmetries for Geometrical Figures Tutorial: Symmetries for Geometrical Figures Example: Identify the lines of symmetry in given figure 12.3 Reflection Tutorial: Reflection

19 Example: Reflection in x axis Example: Reflection in y axis Example: Reflection in x axis & y axis Example: Coordinates of triangle reflected in x axis Example: Find a, b if reflected point is known Rotation Tutorial: Rotation Example: Find point if rotated 90 degree anticlockwise about origin Example: Find point if rotated 90 degree clockwise about origin Example: Find coordinates of if rotated 90 degree anticlockwise about origin Practices Test1 13. Trigonometry 13.1 The Trigonometric Functions Tutorial: The Trigonometric Functions Example1: Given a right triangle, evaluate all six trig functions for the indicated angle Example2: Given a right triangle, evaluate all six trig functions for the indicated angle Example3: Given a right triangle, evaluate all six trig functions for the indicated angle Example4: Given that θ is an acute angle & sec(θ) =a/b, find the other trig. functions Example5: Given π< θ < aπ/b & cos(θ)= c/d, find the other trig. functions Example6: Solve the right triangle (find all sides & all angles) Example7: Given that θ is an acute angle & sec(θ) =u, find the other trig. functions Example8: Given that θ is an acute angle & tan(θ) =a/b, find the other trig. functions 13.2 Heights and Distances Tutorial: Heights and distances Example: Distance of ship from lighthouse (6 Marks)

20 Example: Distance between cars on opposite sides of tower given angles of depression (6 Marks) Example: Find height of tree and width of road (6 Marks) Example: Find angle of elevation (1 Mark) Example: Find vertical distance between 2 aeroplanes (6 Marks) Example: Given angles of depression and distance between 2 ships, find height of light house (6 Marks) Example: Find height of tower given angles of elevation which are complementary (6 Marks) Example: Find speed of aeroplane (6 Marks) Example: Find height of building (1 Mark) Example: Find distance of boat from a point on surface (1 Mark) Example: Find height of tower (2 Marks) Example: Find height of pole (1 Mark) Example: Determine height of billboard (3 Marks) Example: Find angle of elevation of a tower (1 Mark) Example: Find height of tower (1 Mark) Example: Find height of building if observed from tower (6 Marks) Example: Find width of river as observed from helicopter (6 Marks) Example: Find height of tower (Observer height is given) (6 Marks) Example: Find height of pedestal on which a statue is placed (6 Marks) Example: Find height of pillar as seen from other pillar (6 Marks) Example: Find height of tower from top of a building (6 Marks) Example: Find height of the tree Example: Find distance between 2 ships as seen from an aeroplane (6 Marks) Example: Find height of poles on either side of road & distance from point of observation (6 Marks) Example: Find height of tower Example: Find the distance traveled by the balloon during the interval Example: Find the length of the slide Example: Find the length of the string

21 14. Algebraic Expressions and Identities 14.1 Algebraic Expressions Tutorial: Recall Example: Identify the coefficient and variable in the given term (1) Example: Identify the like terms (3) Example: Write the degree, term and coefficient of the given polynomial (2) Example: Write the coefficient of variable from the given expression (1) Example: Identify given algebraic expression as monomial/binomial/trinomial (1) Example: Write the coefficient of given variable (1) Example: Identify given algebraic expression as monomial/binomial/trinomial (1) 14.2 Addition and Subtraction of Algebraic Expressions Tutorial: Addition and Subtraction of Algebraic Expressions Example: Add the polynomials (1) Example: Add the polynomials (1) Example: Add the polynomials (1) Example: Subtract the polynomials (1) Example: Subtract the polynomials (2) Example: Subtract two algebraic expressions (2) Example: Subtract two algebraic expressions (2) Example: Subtract the polynomials (2) Example: Find perimeter of triangle whose sides are in form of binomial expressions (1) Example: Add the algebraic expressions (1) Example: What should be added to trinomial expression to make it binomial expression (3) Example: Add the 3 algebraic expressions Example: Add the algebraic expressions Example: Add the algebraic expressions Example: Add the algebraic expressions Example: Add the algebraic expressions Example: Subtract a polynomial from another

22 Example: Subtract a polynomial from another 14.3 Product of a Monomial and a Polynomial Tutorial: Product of a Monomial and a Polynomial Example: Find the product of a monomial and a polynomial (2) Example: Find the product of a monomial and a polynomial (2) Example: Find the volume of a rectangular box whose dimensions are given (3) Example: Subtract a polynomial from another (1) Example: Find the product of monomials Example: Find the product of monomials Example: Find the area of rectangle whose dimensions are given Example: Complete the table of product Example: Find the volume of a rectangular box whose dimensions are given Example: Find the volume of a rectangular box whose dimensions are given Example: Find the volume of a rectangular box whose dimensions are given Example: Add the polynomials Example: Add the polynomials Example: Subtract a polynomial from another Example: Find the product of monomial & polynomial Example: Complete the table of product Example: Simplify algebraic expression Example: Find the product of monomials Example: Find the value of expression when value of x is given Example: Find the value of expression when value of x is given Example: Subtract a polynomial from another Evaluate Algebraic Expressions Tutorial: Evaluating Algebraic Expressions

23 Example: Evaluate an algebraic expression Example: Evaluate an algebraic expression Example: Evaluate a linear/quadratic expression Example: Evaluate a polynomial 15. Factoring 15.1 Factorisation by Grouping Tutorial: Factorisation by Grouping Example: Find the greatest common factor of the given numbers (1) Example: Find the greatest common factor of the given numbers (3) Example: Factor out the greatest common factor from the given expression (3) Example: Factor out the greatest common factor of given the trinomial (3) Example: Factor out the minus sign from given binomial.(2) Example: Factorize by grouping (5) Example: Factorize by grouping: y^2 + ay + by +c (5) Example: Factorize x^2 + xy + ax + by (2) Example: Find the common factor of given terms Example: Factorise the given expression: ax b Example: Factorise the given expression: pa^2 + qa Example: Factorise the given expression: ax^2y bxy^2 Example: Factorise the given expression: pa^2 qb^2 + tc^2 Example: Factorise the given expression: pa^2 + qab tca Example: Factorise the given expression: apq + b + cq + dp Example: Find the common factor of given terms Example: Factorise the given expression: ax+by ay by Pair of Linear Equation in two variables 16.1 Pair of Equation in two variables Tutorial: Pair of equation in two variables Example: Identify if given point is solution of given system (1 Mark)

24 Example: Represent cost of Items algebraically (1 Mark) Example: Identify if given ordered pair is solution of given system (1 Mark) Example: Write equations of given axis (1 Mark) Example: Find 'a' so that given point lies on the line (1 Mark) Example: Check if given values of x, y are solution of given equation (1 Mark) Example: Express y in terms of x in the given equation and check if given point is on the line (1 Mark) 16.2 Graphical method of solving pair of Linear Equation Tutorial: Graphical method of solving pair of linear equation Example: Find if given pair of linear equations are consistent/inconsistent (2 Marks) Example: Find vertices of triangle formed by the given lines (3 Marks) Example: Find if given pair of equations are consistent/inconsistent & solve graphically (2 Marks) Example: Find 'k' for unique solutions, given perimeter (1 Mark) Example: Check if given pair of equations is parallel, coincident or intersect (2 Marks) Example: Find a,b if given pair of equations have infinitely many solutions (2 Marks) Example: Find dimensions of garden (2 Marks) Example: Without drawing graph determine whether lines will be parallel/intersecting (1 mark) Example: Find 'p' for the system of equations to represent parallel lines (1 mark) Example: Find value of 'k' for system of equations to have infinite solutions (1 Mark) Example: Without solving find if the pair of equations is consistent (1 Mark) Example: Find whether the system of equations has any solutions (1 Mark) Example: Find value of 'k' if system has unique solutions (1 Mark) Example: Write condition for equations to be parallel/coincident/intersecting (1 Mark) Test your skill1 Test your skill Algebraic method of solving pair of linear Equation Tutorial: Algebraic method of solving pair of linear equation Example: Solve using substitution method (2 Marks)

25 Example: Solve for x and y (3 Marks) Example: Applications on age problem (3 Marks) Example: Applications on two digit no (3 Marks) Example: Find 2 numbers from given (2 Marks) Example: Application on two digit number (3 Marks) Example: Application on salary and annual increment (3 Marks) Example: Application on taxi fare (3 Marks) Example: Application on income and expenditure (3 Marks) Example: Application on finding angles of a triangle (3 Marks) Example: Application on questions in a test (3 Marks) Example: Application on upstream/downstream (6 Marks) Example: Application on monthly expenses (3 Marks) Example: Application on finding l and b of rectangle, if area is known (3 Marks) Example: The two given equations have a unique solution, find value of k (2 Marks) Example: Find value of k for which given values of x & y is solution of given equation (1 Mark) Application: Applications on price of item (3 Marks) Application: Applications on % in mixture (3 Marks) Application: Applications on upstream/downstream (3 Marks) Application: Applications on speed (3 Marks) Application: Applications on % in solutions (3 Marks) Application: Applications of currency (3 Marks) Application: Applications of fractions (3 Marks) Application: Applications on library charges (3 Marks) Application: Applications on age problem (3 Marks) 1 2 Test your skill 17. Linear Inequalities 17.1 Linear Inequation Tutorial: Linear Inequation Example: Find the solution set for given inequation (3)

26 Example: Find the solution set for given inequation (2) 17.2 Solutions of Linear Inequalities Tutorial: Solutions of Linear Inequalities Example: Solve inequality & graph the solution (3) Example: Solve inequality & graph the solution (3) Three Part Inequalities Tutorial: Three Part Inequalities Example: Solve inequality & graph the solution (3) Example: Solve inequality & graph the solution (2) Relations and Functions 18.1 Definition of a Relation Tutorial: Definition of a Relation Example1: Find the domain and range of a relation defined by a given set of points 18.2 Definition of a Function Tutorial: Definition of a Function 18.3 Graph of a Relation Tutorial: Graph of a Relation Example1: Graph y = mx + c Example2: Graph ay^2 = bx Example3: Graph y = x + a 18.4 Vertical Line Test Notation Tutorial: Vertical Line Test Example1: Determine if a graph represents a function 18.5 Functional Notation f(x)

27 Tutorial: Functional Notation Example1: Compute f(a), f(b) 18.6 Section Review Practice 18.6 Additional Examples with Pop up Solution Example: Identify whether the relation is a function? Also find domain & range in each case (0110) Example: Determine whether or not the equation ax+by=c describes a function (1517) Example: Determine whether or not the equation y=a describes a function (1824) Example: Determine whether or not the equation ax+by=c describes a function (1928) Example: Determine whether or not the equation y^2=ax describes a function (2025) Example: Determine whether or not the equation y=1/(ax+b) describes a function (2627) Example: Determine whether or not the equation y=ax/(x^2+b) describes a function (2930) Example: Identify whether or not the relation defined by graph is a function (3143) Example: Identify whether or not the relation defined by graph is a function (3444) Example: Find the indicated value given f(x)=ax^2 bx+c (4551) Example: Find the indicated value given g(x)= ax (4756) Example: Find the indicated value given f(x)=a/(x^2+b) (5257) Example: Find the indicated value given g(x)= (x+a)^2 (5455) Example: Find the indicated value given f(x)=(a/b)x^2+(c/d)x e (5862) Example: Find the indicated value given g(x)=(x^2+a)/ b (5961) 19. Graphs of Linear/Non Linear Functions/Equations 19.1 Plotting Ordered Pairs Tutorial: Graph Order Pairs Example: Plot (a,b) Example: Given the plot of a point, find its coordinates 19.2 Graphing a linear equation using points Tutorial: Graphing a linear equation using points Example: Graph px + qy = r 19.3 Graphing a linear equation Using intercepts

28 Tutorial: Using intercepts to Graphing a linear equation Example: Plot px + qy = r by plotting its intercepts 19.4 Slope of a Line Through Two Given Points Tutorial: Slope of a Line Example1: Find the slope of the line through (a,b), (c,d) and graph it Example2: Given m, determine the type of y = mx + c Example: Identify slope of a line from its graph 19.5 Finding the slope of a line from the equation of the line Tutorial: Finding the slope from the equation of the line Example: Find the slope of a line Example2: Find the slope of ax + by + c = Solutions of Linear Inequalities Tutorial: Solutions of linear inequalities Example: Graph an inequation on a number line Example: Graph (3 + 4x) is less than (3x + 11) on a number Example: Graph 4x 16 on a number Example: Graph ((3/4)x 4) is less than ((4/5)x + 1) on a number Example: Write a statement as an inequality Example: Write a statement as an inequality Example: Graph the solution (4) is less than (2x) is less than (6) on a number Example: Graph ( 3) (1 2x) 6 on a number Example: Solve an inequality ( 12) (4 (3/ 5)x) is less than (2) Example: Solve a word problem on an inequality 19.7 Graphing Linear Inequalities in two Variables Tutorial: Graphing linear inequalities in two variables Example: Graph the solution of (2x y) is greater than (3) 19.8 Solving System of Linear Inequalities Tutorial: Solving system of linear inequalities Example: Graph the solution of the given system of linear system of equations Example: Graph the solution of the given system of linear system of equations

29 20. Statistics and Probability 20.1 Statistics Tutorial: Statistics 20.2 Presentation of Data Tutorial: Presentation of Data (2) Example: Find range of the given data 20.3 Graphical Representation of Data Tutorial: Graphical Representation of Data Tutorial: Graphical Representation of Data Example: Answer from the histogram (salary) (3) Example: Read the circle graph.(1) Example: Read the circle graph.(4) Example: Construct the circle graph to represent th given data.(5) Example: Read the bar graph.(2) Example: Read the bar graph.(3) Example: Read the bar graph.(3) Example: Construct the bar graph using the given data.(4) Example: Construct the bar graph using the given data.(4) Example: Read the graph.(3) Measure of Central Tendency Tutorial: Measure of Central Tendency Example: Find mean of primes less than given number (2)

30 Example: Find mode of given data (basketball team) (1) Example: Find median of given data (2) Example: Find x if mode is given (1) Example: Find x if median is given (2) Example: Find x if mean is given (2) Example: Find median after finding mean (3) Example: If mean of values in x is known, find mean of first three values (3) Example: Find excluded number if mean is known (2) Example: Find value of p if mean of data is known (4) Example: Find nth observation if mean is known (2) Example: Find mean weight (2) 20.5 Mean of Grouped Data Tutorial: Mean of Grouped Data Example: Find mean of increased values (2) Example: Find n if sum of deviations is known (3) Example: Find mean using step deviation method (3) Example: Find missing frequency (4) Example: Find missing frequencies if mean & total frequency are known (5) Example: Find frequency of given class interval (1) Example: Find sum of deviations from mean (1) 20.6 Mode of Grouped Data Tutorial: Mode of Grouped Data Example: Find mode of given data (3) Example: Find missing frequencies if mode & total frequency are known (5) Example: Find mode of given data (3) Example: Find mode of given data (1) Example: Find lower limit of modal class (1)

31 Example: Find modal life of components (4) 20.7 Median of Grouped Data Tutorial: Median of Grouped Data Example: Find median of given data (4) Example: Find missing frequencies, if median is known (5) Example: Calculate median (less than) (4) Example: Find the median of the given data (1) Example: Find mean if mode & median are known (2) Example: Find mode if mean & median are known (3) 20.8 Probability Tutorial: Probability Example: Probability when die is thrown (1 Mark) Example: Find probability of drawing a particular ball (1 Mark) Example: Find probability of selecting boy/girl (1 Mark) Example: Find x, if probability of drawing a ball is given (2 Marks) Example: Find probability of a specific day in non leap year (2 Marks) Example: Find probability of getting prize winning ticket (1 Mark) Example: Find probability of choosing a consonant/vowel (1 Mark) Example: Find probability of getting a specific day in a leap year (2 Marks) Example: Probability of birthday problem (1 Mark) Example: Find probability of drawing 2 digit number from a box (1 Mark) Example: Probability of game of spinning arrow (1 Mark) Example: Probability of tossing 3 unbiased coins (1 Mark) Example: Probability of die landing in a circle (1 Mark) Example: Probability of ball in roulette wheel (1 Mark) Example: Probability of raining on a day (1 Mark) Example: Probability if coin is tossed three time (1 Mark)

32 Example: Probability of atleast 2 boys (2 Marks) Example: Problem of coloured balls (2 Marks) Example: Probability of drawing a card (1 Mark) Example: Probability of drawing non defective nut (1 Mark) Example: Find (1 P(Ē)) (1 Mark) Example: Probability on throwing a die (1 Mark) Example: Probability of drawing a ball (1 Mark) Example: Write sample space for balls (1 Mark) Example: Check for probability (1 Mark) Example: Probability of drawing a card (1 Mark) Example: Find the probability of that the coin will be a 50p coin/ will not be a Rs 5 coin Example: What is the probability that the fish taken out is a male fish? Example: Find the probability that the bulb is not defective Example: Find the probability of getting a card of heart, king, club etc. Example: Find the probability of getting exactly two heads Example: What is the probability that the sum of two numbers appearing on the top of dice is n Example: What is the probability that the two friends visit the shop on same day? Example: What is the probability that the total score on die is even Example: Find the number of blue marbles in the jar Example: A dice is thrown. What is the probability that a given no. will come up atleast once 21. Vectors 21.1 The Position Vector Tutorial: The Position Vector 21.2 The Representations of a Position Vector Tutorial: The Representations of a Position Vector 21.3 The Magnitude (Norm) of a Vector Tutorial: The Magnitude (Norm) of a Vector Example1: Find the magnitude of the given vector in component form Example2: Find the magnitude of the given vector in vector form

33 21.4 Vectors with Magnitude and Inclination Tutorial: Vectors with Magnitude and Inclination Example1: Given the magnitude and inclination of a vector, find the vector 21.5 Addition of Vectors Tutorial: Addition of Vectors Example1: Find the sum vector of two given vectors 21.6 Multiplication by a Scalar Tutorial: Multiplication by a Scalar Example1: Given vectors u, v find au + bv 21.7 Vectors with Initial Points not at the Origin Tutorial: Vectors with Initial Points not at the Origin Example: Given points P, Q; write the vector PQ in numeric form 21.8 The Unit Vector Tutorial: The Unit Vector Example: Find the unit vector in the same direction as a given vector Example: Find a unit vector parallel to a given vector Example: Find the resultant force acting on the object 22. Matrices 22.1 Matrices Tutorial: Matrices Example: Find dimension of given matrix (1) Example: Construct a 2*3 matrix whose elements are given by aij = (i + r)(j + t), i =1, 2 ; j = 1, 2, 3 (2) Example: Construct a 2*3 matrix whose elements are given by aij = ci dj, i =1, 2 ; j = 1, 2, 3 (2) Example: Construct a 2*2 matrix whose elements are given by aij = ( i + j )^2 / t, i =1, 2 ; j = 1, 2 (2) Example: Construct a 3*2 matrix whose elements are given by aij = i 3j / t, i =1, 2, 3 ; j = 1, 2 (2) Example: Construct a 3*2 matrix whose elements are given by aij = ( i + 2j )^2 / t, i =1, 2, 3 ; j = 1, 2 (2)

34 22.2 Equality of Matrices Tutorial: Equality of Matrices Example: Find x,y,a and b from two given matrices (2) Example: Find the values of x and y from two equal matrices (3) Example: For what real values of x and y the given matrices A & B are equal (3) Example: Find the values of x, y and z from two equal matrices (2) Example: Find the values of x, y and z from two equal matrices (3) Example: Find the values of a, b, c and d from two equal matrices (4) 22.3 Addition of Matrices Tutorial: Addition of Matrices Example: Find sum of two matrices (2 x 2) (2) Example: Find sum of two matrices (2 x 3) (2) Example: Find sum of two matrices (2 x 2) (2) Example: Given matrices A and B, find the matrix C if A + B C = 0 (2) 22.4 Subtraction of Matrices Tutorial: Subtraction of Matrices Example: Find difference of two matrices(3 x 3) (2) Example: Given matrices A, B, C, find value of A B+C (2) Example: Given matrices A and B, find matrix C s.t. A B+C = 0 (2) Example: Find matrix x if sum of two matrices is given (2) 22.5 Matrix Multiplication Tutorial: Matrix Multiplication Example: Multiply (1 x 3) & (3 x 1) matrices (2) Example: Multiply (1 x 3) & (3 x 1) matrices (2)

35 Example: Find (x,y) entry of AB, given A, B (2) Example: Multiply two 2 x 2 matrices (2) Example: Find product of (3 x 2) and (2 x 3) matrices (3) Example: Application on unit price of TV set (2) Example: Find AI &IA where A is 3 x 3 matrix (2) Example: Given matrices A and I, find values of x and y s.t (xi + ya)^2 = A (4) Example: Given matrices A and I, find value of k so that A^2 = ka ni (3) Example: Write as a single matrix by simplifying the matrices (2) Example: Given matrix F(x), examine whether F(x)F(y) = F(x + y) or not (3) Example: Given matrices A & B, find value(s) of α for which A^2 = B (if it exists) (2)